[662] Paper
Majority Rules and Incentives
International voting affects domestic
policies
Bård Harstad
No. 662 – 2004
Norwegian Institute
of International
Affairs
Norsk
Utenrikspolitisk
Institutt
Utgiver: NUPI
Copyright: © Norsk Utenrikspolitisk Institutt 2004
ISSN: 0800 - 0018
Alle synspunkter står for forfatternes regning. De må
ikke tolkes som uttrykk for oppfatninger som kan
tillegges Norsk Utenrikspolitisk Institutt. Artiklene
kan ikke reproduseres - helt eller delvis - ved
trykking, fotokopiering eller på annen måte uten
tillatelse fra forfatterne.
Any views expressed in this publication are those of
the author. They should not be interpreted as
reflecting the views of the Norwegian Institute of
International Affairs. The text may not be printed in
part or in full without the permission of the author.
Besøksadresse: C.J. Hambrosplass 2d
Addresse: Postboks 8159 Dep.
0033 Oslo
Internett: www.nupi.no
E-post: [email protected]
Fax: [+ 47] 22 36 21 82
Tel: [+ 47] 22 99 40 00
Majority Rules and Incentives
International voting affects domestic
policies*
Bård Harstad
*
I am indebted to Torsten Persson for carefully reading several drafts. I have also
benefited from the comments by Philippe Aghion, Geir B. Asheim, Patrick Bolton,
Guido Friebel, Oliver Hart, Jo Thori Lind, Arne Melchior, seminar participants at IIES,
Kellogg School of Management, Pennsylvania State University, Princeton University,
Stockholm School of Economics, Stockholm University, the University of Bergen, the
University of Oslo, the European Winter Meeting of the Econometric Society (2003)
and the Conference on Current Trends in Economics (2003). Thanks to Christina
Lönnblad for editorial assistance. The Tore Browaldh Foundation and the Norwegian
Research Council provided financial support.
Key words: Collective decisions, voting rules, reforms, hold-up problem, delegation
JEL Classification: D71, H77, H11
[Abstract] A "majority rule" defines the number of club-members that must approve a
policy proposed to replace the status quo. Since the majority rule thus dictates the extent to
which winners must compensate losers, it also determines the incentives to invest in order to
become a winner of anticipated projects. If the required majority is large, the members invest
too little because of a hold-up problem, if it is small, the members invest too much in order
to become a member of the majority coalition. To balance these opposing forces, the
majority rule should increase in the level of minority protection (or enforcement capacity)
and the project’s value but decrease in the ex post heterogeneity. Strategic delegation turns
out to be sincere exclusively under this majority rule. Externalities can be internalized by
adjusting the rule. With heterogeneity in size or initial conditions, votes should be
appropriately weighted or double majorities required. The analysis provides
recommendations for Europe’s future constitution.
1. Introduction
If everyone agrees, collective decisions are taken unanimously. Unfortunately, whenever
some gain from a public project, others typically lose. A common solution is to apply a
"majority rule", defined as the fraction of agents that must approve a policy proposed to
replace the status quo. The majority rule thus determines the extent to which winners of
a project must compensate losers. Whether an agent really is a winner depends on her
action and preparation in advance. In this paper, I investigate the incentive to make such
investments and find how it is distorted by the majority rule. Moreover, I argue that the
concern for incentives should be decisive when voting rules are chosen, and the optimal
majority rule is characterized.
While this problem is quite general, the debate on majority rules might currently be
hottest in Europe. The European Council applies different majority rules to different
issues. Procedural questions can be taken by simple majorities, issues related to the
common market require a qualified majority, and foreign policies unanimity. This raises
the positive question of why majority rules differ across issues.1 Historically, majority
rules have been debated in the EU since it was founded. The Treaty of Rome (1957)
intended to use majority voting for most issues, but the Luxembourg Compromise (1966)
effectively gave each member a veto for issues of "vital interest". After a halt in the
integration process, the Single European Act (1986) established qualified majority voting
for issues related to the internal market. The range of issues to which majority voting
applies was further extended by the Maastricht Treaty (1992) and the Treaty of Nice
(2000). Last summer, the European Convention completed its Draft for the EU’s future
constitution. The Convention suggests that qualified majority voting should be extended
to several issues that required unanimity in the past. Furthermore, "qualified majority"
should be redefined from 71% to 60%. The Draft has led to fierce negotiations which seem
to continue throughout 2004. It is thus both important and timely to raise the normative
question of what are the optimal majority rules.2
A typical project in the EU is to liberalize its common market. Quite soon, we might
see additional directives on the liberalization of public utilities (electricity, telecom, mail,
transport). Though the EU has already taken several steps towards such liberalization,
much remains to be done. CEPR (1999, p.1) reports that full liberalization of the European electricity market will provide substantial gains amounting to 10-12 billion Euro per
annum, or twice as much as the gains anticipated from the opening already agreed. It is
evident that different countries have quite different values of such liberalization; the UK,
for example, supports it solidly. This is not accidental, but thanks to Thatcher’s privatization effort in the 1980s. Similarly, a country’s future value of liberalization depends
on its policy today. CEPR (1999) criticizes countries for different standards, bad market
institutions, public ownership and state aid. Unless the member countries make the appropriate policies today, liberalization might be impossible tomorrow. But do countries
have right incentives to invest, or do they fear to be held up by others? How do the
incentives depend on the majority rule? What determines the optimal rule?
This paper provides a three-stage model of collective decisions. At the constitutional
1
2
For the current rules, see e.g. Hix (2004).
For the Convention’s suggestion, see http://european-convention.eu.int.
2
stage, members of a club select a majority rule. At the investment stage, each member makes some non-contractible investment which thereafter affects her value of the
anticipated public project. The values may also be affected by individual and aggregate
shocks. At the legislative stage, a majority coalition is formed which proposes a set of
side payments and whether the project should be implemented. The proposal is executed
if approved by the required majority.
Solving the game by backward induction, we can derive the legislative outcome, equilibrium investments and the optimal majority rule. It is shown that when transaction
costs vanish, the project is implemented if and only if it is socially efficient ex post whatever is the majority rule. This is because the majority coalition captures the entire
value of the project if it is implemented, while it fully expropriates the minority in any
case. This result resembles the Coase Theorem, and it suggests that the importance of
majority rules may not be to select the right projects.
At the investment stage, the members face two strategic concerns. On the bad side,
investments reduce bargaining power. Members happening to be winners of the project
become very eager to see it implemented and, in equilibrium, they are expropriated or must
compensate those benefiting less. This is a multilateral hold-up problem which discourages
investments. On the good side, investments increase a member’s probability of obtaining
political power, since the winning majority coalition will consist of the members most in
favor of the project. This is valuable, since it is the majority coalition that determines the
distribution of surplus. If the majority rule is small, political power is very beneficial, since
few losers need to be compensated and a large minority can be expropriated. To improve
the chances of become a member of the majority coalition, each member invests too
much. If the majority rule is large, political power is less attractive, the hold-up problem
dominates, and members invest too little. To balance these two opposing forces, the
majority rule should depend on the club’s enforcement capacity (or minority protection),
and the particular project’s expected value and heterogeneity in values.
Besides providing insight itself, this simple model is employed as a framework for
studying several related issues. In particular, each member may be tempted to strategically delegate bargaining authority to either a reluctant delegate to increase bargaining
power, or to an enthusiastic delegate to gain political power. It is shown that delegation is
sincere exclusively at the optimal majority rule. Externalities related to the investments
can be internalized by adjusting the majority rule. The legislative game is generalized
to discuss the effects of bicameralism, presidency and rotating political representation
(as suggested by the European Convention). If members are of different size, first-best
investments are implemented by either weighted votes (the weights should be regressive
in a member’s size) or double majorities, in combination with rotating political representation (larger members should be represented with larger probability). Heterogeneity
in initial conditions generates asymmetric and suboptimal investment levels, though also
this problem can be solved by either weightening the votes or using double majorities.
The model is general and relevant for a wide range of collective decisions in both
public economics and corporate governance.3 Still, the European Union appears to fit
tightly to the description. The policy space in the EU is typically unidimensional (further
3
See the final section for some examples.
3
integration vs. the status quo) and decisions are taken by a combination of voting,
negotiations and side payments. In line with the model, Kirchner (1992, p. 134) describes
that package deals are built on coalitions among like-minded governments and often involve
trade-offs or side-payments. As he notices, side payments can be implicit in the form of
logrolling, issue linkages or by just redefining the project. Or, they can be explicit:
"Structural funds" arose to compensate the UK for the Union’s agricultural expenditures
(in 1969), they were doubled to convince the Mediterranean countries to accept the Single
European Act (1986), and "cohesion funds" were invented to compensate poorer members
for the tough financial criteria imposed by the Maastricht Treaty (1992).4 When applied
to the EU, several of the model’s predictions are supported. On the normative side, the
analysis provides recommendations for its future constitution.
The theoretical debate on majority rules is certainly older than the European Union.
Already Rousseau (1762) contrasted unanimity to rules requiring smaller majorities, and
Condorcet (1785) is famous for his Jury Theorem; advocating the simple majority rule as
the best way of aggregating information. More than a century ago, Wicksell (1896) advocated unanimity as the only rule guaranteeing Pareto improvements. However, Buchanan
and Tullock (1962) argued that the majority rule should trade off the costs of expropriating the minority (emphasized by Wicksell) against "decision-making costs", increasing
with the majority rule. They did not, though, clarify what these decision making costs
are. Recently, and more formalized, Aghion and Bolton (2003) take the winners’ wealth
constraints into account, and minimize the costs of expropriating the minority subject to
the budget constraint in order to derive the optimal majority rule. A similar trade-off
is studied by Aghion, Alesina and Trebbi (2004) who, in addition, point to the costs of
compensating losers.5
As discussed by Mueller (1989), controversies in the literature on majority rules often
arise from different assumptions on whether side payments are allowed, and at which
transaction costs. Some transaction costs are typically assumed since otherwise, the Coase
Theorem holds and the majority rule becomes irrelevant for the selection of projects (as in
this paper). A larger caveat with the traditional literature, in my view, is that individual
values are just exogenously given. Whether you are a winner or a loser of the project
is simply drawn by Nature. The main contribution of this paper is to let the members
influence their future value of the project. The incentives to invest depend on the majority
rule, and the majority rule should be set such that the incentives are right.
Hold-up problems are certainly studied elsewhere in the literature. Suggested institutional remedies include appropriate allocations of ownership (Grossman and Hart,
1986),6 authority (Aghion and Tirole, 1997) and status quo (Aghion, Dewatripont and
Rey, 1994). In international contexts, the importance of the hold-up problem is recog4
For more on this, see George and Bache (2001).
Other aspects of the majority rule are also studied. An early strand of literature (surveyed by
Enelow, 1997) emphasizes Condorcet cycles, and argues that the majority rule should be sufficiently
large to prevent cycles. Barbera and Jackson (2004a) examine majority rules that are stable and induce
agents to select themselves as a decision rule. Maggi and Morelli (2003) observe that majority rules must
be enforced and derive the best enforceable majority rule. The literature is far too large to survey in
this paper - see instead Chapters 4-8 in Mueller (1989). To my knowledge, no other paper focuses on
incentives.
6
Hart and Moore (1990) study optimal ownership in a multilateral hold-up problem.
5
4
nized by e.g. McLaren (1997) who shows how prior adjustments to trade liberalization
may dramatically reduce a country’s bargaining power. Wallner (2003) similarly suggests
that a hold-up problem hurts potential entrants to the EU, which undertake reforms prior
to acceptance. The present paper contributes to the literature on the hold-up problem by
showing how multilateral hold-up problems can either arise or be mitigated, depending
on the particular majority rule.
The effects of political regimes on incentives are discussed by several recent papers.
Persson and Tabellini (1996) study how regional moral hazard depends on whether interregional distribution is decided by voting or bargaining. Anderberg and Perroni (2003)
argue that the majority’s power to choose taxes induces agents to imitate the majority.
Relative to unanimity, majority voting can therefore support an equilibrium where a small
majority save, since it is then time-consistent for them to select a small tax on capital.
In a context with incentives, the particular choice of majority rule is, to my knowledge,
only discussed by Persico (2004). He focuses on searching increasing information on the
project’s common value. The probability of becoming a pivotal voter determines the incentives to search for such information. These incentives are vastly different from the
incentives to invest in private values, studied here.
This paper is also related to an entire literature on delegation. The incentive to
appoint a reluctant delegate in order to strengthen bargaining power is recognized already
by Schelling (1956). On the other hand, Baron and Ferejohn (1989) find that legislators
with low bargaining power have better chances of becoming coalition members. Chari,
Jones and Marimon (1997) discuss how this induces voters to elect representatives too
enthusiastic about the public good. Brueckner (2000) finds these incentives to depend on
the extent to which unanimity is required. I take his point further by investigating how
the majority rule affects the incentives to delegate. In this paper, members may want
to delegate in order to gain either bargaining power or political power. These opposing
incentives are balanced by the optimal majority rule.
The remainder of the paper is organized as follows. The next section presents a simple
model of collective decisions. Section 3 solves this game by backward induction: incentives
are found to depend on the majority rule, and the optimal rule is characterized. This
workhorse model is then employed to discuss strategic delegation, externalities, legislative
games, and heterogeneity in size and preferences. To review, Section 5 contrasts all the
results to the case without side payments. Future research is outlined in the final section.
2. The Model
A club is a set I of members. On day 0, the constitutional stage, the members select a
majority rule m ∈ (0, 1], defining the required fraction of members that must approve a
policy on day 2 proposed to replace the status quo. Since all members are identical at
this stage, they all prefer the same majority rule.
On day 1, the investment stage, each member i ∈ I makes some non-contractible
investment xi at the private cost c(xi ). The function c is increasing, convex, and continuous differentiable. The purpose of this investment is to increase the benefit or reduce the
cost of a particular public project that may be undertaken on day 2. Formally, after the
5
investments have been chosen, member i’s net value of the project is drawn to be
vi = xi +
i
+ θ,
(2.1)
where i and θ are some individual and aggregate shocks, respectively.7 The i s are
independently drawn from a uniform distribution with mean zero and density 1/h:
¸
·
h h
.
i iid v U − ,
2 2
If all members invest the same amount, the realizations of the i s determine the heterogeneity in preferences. If I is finite, the distribution of the i s can take many forms,
making the analysis quite complex. To simplify, I assume that there is a continuum of
members, I ≡ [0, 1], such that the distribution of the i s is deterministic and uniform.8
Then, h measures the ex post heterogeneity in values.9
The state of the world θ measures both the average and the expected value of the
project without investments. θ may be negative, since it includes the cost of the project.
Together with the investments, θ determines whether the project is worthwhile implementing on day 2. To get explicit solutions, also θ is assumed to be uniformly distributed:10
h
σi
σ
.
θ ∼ U a − ,a +
2
2
a is the value of an average project (without investments), and σ measures the standard
deviation in the aggregate shock.11
After the members’ values have been observed by everybody, the legislative stage
begins on day 2. I separate the coalition formation stage, the negotiation stage and the
voting stage. First, the majority coalition is formed. In line with Riker (1962), I assume
that a randomly drawn initiator (or president) selects a minimum winning coalition M ⊂ I
of mass m to form the majority, and that this is all the initiator is doing.12 This is not
important; the initator will simply select the unique core at this stage. Thereafter, the
members of M negotiate a political proposal. All members of the majority coalition must
agree before the proposal is submitted for a vote.13 A proposal specifies whether the
project should be implemented as well as a set of individual
transfers or taxes ti . These
P
taxes must fulfill the budget constraint, which is i∈I ti = 0 if transaction costs are
negligible. The cost of the project, remember, is included in parameter θ. Third, the vote
takes place. Two conditions must be met for the proposal to be implemented. Crucially,
7
For simplicity, I let the different effects be additive. Any multiplicative effect, θxi or i xi , would give
the same results.
8
I here apply the "standard abuse of the law of large numbers", since the distribution of idiosyncratic
shocks never can be deterministic. See Green (1994) for more on this.
9
Footnotes 32 and 48 discuss how the results would change if I were finite.
10
Footnotes 28, 29 and 54 discuss the outcome if the shocks were bell-shaped distributed.
11
To be precise, the variance of θ is σ 3 /12.
12
Section 4.3 relaxes both these assumptions. Then, M might be of a different size than m, and the
initiator may have agenda setting power.
13
That only M can make political proposals might reflect what Baron (1989) labels "coalition discipline". Without such discipline, he argues, the mass of M is likely to be larger than m. This is indeed
proven by Groseclose and Snyder (1996).
6
Figure 2.1: Timing of the game
it must be approved by a mass m of members. Otherwise, all members receive the status
quo payoff of zero (added to their sunk cost of investment c(xi )). A minimum winning
coalition M of size m can therefore dictate the policy to some extent. But there is a
lower boundary r for the minority’s disutility. The proposal must namely be accepted
by all members, in the sense that no member should prefer to deviate and "break" the
constitution to avoid implementing the project. If some members cheat in this way, the
policy will remain at status quo, though the deviators receive their reservation utility −r.
The r might be interpreted as the fine deviators must pay. In some cases, r might be a
constitutional parameter, limited in order to protect minorities. In the EU, for example,
the Luxembourg Compromise of 1966 allows a country to veto a proposal if it threatens
its "vital" interests. In other cases, r might be limited by enforcement capacity. If the
club’s enforcement capacity is created by repeated interaction and trigger strategies, where
deviation today terminates cooperation forever (as in Maggi and Morelli, 2003), then r
reflects a member’s present value of continued cooperation.14 In any case, the project is
accepted and implemented if and only if the members’ payoffs relative to the status quo,
ui = vi − ti ,
are positive for a mass m of members, and larger than −r for all.
3. The Solution
This section solves the game by backward induction to derive its unique subgame-perfect
equilibrium. As a benchmark, observing the first-best outcome is worthwhile. Social
efficiency is defined by the sum of utilities, or, equivalently, as a member’s expected
utility. At the legislative stage, executing the project is optimal if and only if the project
is "good", meaning that its total value is positive:
Z
vi di = θ + x ≥ 0,
(3.1)
I
P
t
If days 1-2 are repeated every year, then r ≡ ∞
b} − c(b
x)] where δ is the yearly
t=1 δ [E max{0, θ + x
discount factor, x
b the equilibrium investment, and where it is anticipated that (i) the project is implemented if and only if it is good (θ + x
b ≥ 0) and (ii) these gains are expected to be evenly spread across
the members. This makes the enforcement capacity r an increasing function of the discount factor δ.
14
7
where x denotes average investment.15 Thus, the probability q that the project turns out
to be good ex post is increasing in x:
a+ σ2
q(x) ≡
Z
dθ
1
1
= (a + x) + .
σ
σ
2
−x
Under the optimal selecting rule (3.1), the optimal effort level at the investment stage is
determined by
a+ σ2
Z
dθ
Max E
− c(x) ⇒
(θ + x + i )
x
σ
−x
c0 (x∗ ) = q(x∗ ).
(3.2)
The second-order condition is σc00 (x∗ ) ≥ 1, which I assume to be fulfilled.16
3.1. Majority Rule Irrelevance
Let us now solve the final legislative stage of the game. To maximize its surplus, any
majority coalition M will ensure that all members of the minority N ≡ I\M receive
exactly their reservation utility of −r. This is achieved by setting taxes such that
ti = vi + r ∀i ∈ N
if the project is proposed, and by setting ti = r∀i ∈ N otherwise. If any i ∈ N obtained
less utility, that member would not accept the policy and the majority would receive
nothing. If any i ∈ N obtained more than −r, that member could be taxed more and
these revenues could be distributed within the majority. Thus, the majority coalition
is taxing a member i ∈ N more if vi is large, since i is then more willing to accept the
proposal. This negative effect of a larger vi on ti may be interpreted as a loss of bargaining
power, and it completely nullifies the positive direct effect of vi on ui : for i ∈ N, ui = −r ,
notwithstanding vi .
As discussed in the Introduction, most of the literature on majority rules presumes
that transaction costs arise whenever some members are taxed. Before I let them vanish, I
will now introduce small transaction costs, for two reasons. First, this allows us in a simple
way to relate Proposition 1 below to the existing literature. Second, it allows us to derive
Axelrod’s (1970) hypothesis of minimum connected winning coalitions, meaning that M
consists of those i with the highest vi (if the project is good). This coalition formation
is simply assumed by e.g. Aghion and Bolton (2003). Many kinds of transaction costs
give us the same result,17 but for simplicity I follow Aghion and Bolton (2003). For each
15
For this and similar integrals to be defined, vi is assumed to be piecewise continuous in i.
The optimal x∗ is only implicitly defined by (3.2). If c(x) = kx2 /2, the explicit solution for x∗ is
∗
x = (a + σ/2) / (kσ − 1) and the second-order condition is 1 − kσ ≤ 0. If instead 1 > kσ, then (3.2)
shows the ArgM in w.r.t. x.
17
To be precise, any pair of transaction cost functions for compensation and taxes, where the deadweight
loss is (weakly) convex in the amount of transfers, leads to the following results. The results also hold
whenever it is no more costly (deadweight loss) to tax (compensate) the majority (minority) than the
minority (majority).
16
8
unit expropriated by the minority, a fraction λ measures the deadweight loss. The total
surplus available for the majority is then
Z
Z
vi di + (vi + r)(1 − λ)di,
(3.3)
M
N
if the project is proposed.18 Otherwise, the total surplus for the majority is
Z
r(1 − λ)di.
(3.4)
N
The allocation of this surplus is determined by multilateral negotiations within the majority coalition. If the negotiations fail, the status quo remains. Though it might not be
obvious how to define the bargaining game with a continuum of players, I let the outcome
be characterized by the Nash bargaining solution for a finite number of players.19 This
outcome coincides with the Shapley value when all coalition members have veto power,
and it is a likely outcome of non-cooperative bargaining.20 It ensures that all members of
the majority coalition receive the same surplus. This is achieved when coalition members
with large vi s subsidize coalition members with lower vi s. Intuitively, a coalition member
with a high value vi has correspondingly low bargaining power, since she is eager to implement the project. Other members are then able to hold up i by requiring side payments
to accept the project. As for bilateral negotiations, the value of cooperation is equally
shared. As were the case for minority members, also majority members lose bargaining
power when vi is large, and this negative effect neutralizes the positive direct effect of vi
on ui : for i ∈ M, ui is the same, notwithstanding vi .
If the initiator does not find implementing the project worthwhile, all minority members will be taxed by r, and the majority’s surplus (3.4) is independent of the composition
of the majority coalition. Suppose then that the initiator selects coalition members randomly. If the project is to be implemented, instead, any initiator prefers to form the
18
It is here implicitly assumed that vi + r ≥ 0∀i ∈ N .
Nash’s axiomatic theory for bilateral bargaining extends unchanged to multilateral situations. Since
the default outcome gives zero utility for all, the Nash bargaining outcome follows from maximizing the
Nash product
Y
X
X
M ax
(vi − ti ) s.t.
ti = −
(1 − λ)ti
19
{ti }i
i∈M
i∈M
and s.t. vi − ti
i∈N
≥ −r ∀i ∈ N ,
if the number of agents is finite and their utilities transferable. This ensures that all agents in the majority
coalition receive the same utility vi − ti . Utilities are transferable within the coalition only if there are
negigible transaction costs in transferring surplus within the majority. This is assumed by Aghion and
Bolton (2003).
20
In general, there exist multiple subgame-perfect equilibria to multilateral bargaining situations. Krishna and Serrano (1996) allow each player to exit with its share of the surplus following some proposed
allocation. Then, they obtain a unique equilibrium outcome coinciding with the multilateral version of
the Nash bargaining solution when the discount factors between successive offers approach one (see their
Theorem 1’). In this outcome, everyone receives the same utility if utility is transferable. A similar
justification is provided by Hart and Mas-Colell (1996).
9
majority coalition with the members having the highest possible values vi s, since this
maximizes (3.3).21 These "winners" of the project do not need to receive (much) compensation to approve the project; they are instead ready to compensate others.22 Thus,
there is a positive effect of vi on i’s political power. If the members undertake the same
investment x on day 1, individual values on day 2 will be uniformly distributed with the
mean θ + x and density 1/h. The majority coalition will consist of the upper m fractile
of this interval, i.e. [vm , θ + x + h/2], where23
¶
µ
1
−m .
vm ≡ θ + x + h
2
Hence, if the project is going to be implemented, member i’s political power is given by
i ∈ N if vi < vm and m < 1
i ∈ M if vi ≥ vm or if m = 1.
Thus, the majority coalition consists of members with similar preferences (in line with
Axelrod, 1970), namely those with the highest value of the public project.24
By comparing (3.3) and (3.4), the majority coalition will implement the project if and
only if
Z
Z
Z
vi di + (1 − λ)(vi + ri )di ≥
(1 − λ)ri di ⇒
M
Z
M
N
vi di +
Z
N
(1 − λ)vi di ≥ 0.
N
Since the lowest values vi are discounted by (1 − λ), the majority may implement the
project even if it is not socially optimal. Partly for this reason, Wicksell (1896) recommended that decisions should be taken by unanimity. However, Buchanan and Tullock
(1962) argued that this would create large decision-making costs, though they did not
specify what these costs might be. Aghion and Bolton (2003) assume that wealth constraints make the project impossible to finance if all losers must be compensated. As all
21
This coalition of "winners" is thus the unique core of the game (when side payments cannot be
promised, or the coalition shares the surplus equally).
22
To some extent, the winners’ surplus could be expropriated even if these were in the minority, but
parts of these tax revenues would disappear as transaction costs. Moreover, as in the model by Aghion
and Bolton (2003), there might beR some binding
limit w on how large the taxes can be, making the total
R
surplus for the majority equal to M vi di + N wdi. Such a limit could be interpreted as another form of
transaction costs. The surplus expropriated from the minority would then be fixed w(1 − m), while the
coalitions’ surplus would increase in each vi , i ∈ M . Even with an arbitrarily small probability for such
a limit on taxation, the initiator strictly prefers to select the members with the highest vi as coalition
members.
23
The initiator may of course have a low value of the project, since she is randomly drawn from the
entire population, but her size is negligible.
24
This result is similar to the result of Ferejohn, Fiorina and McKelvey (1987), who find that the
majority coalition consists of those legislators with the lowest cost of their project.
10
transaction costs vanish, however, the condition for implementing the project becomes
Z
Z
lim vi di + (1 − λ)vi di = θ + x ≥ 0,
λ→0
M
N
which coincides with the social optimal condition (3.1) - whatever the majority rule is!
Without transaction costs, the majority coalition captures the project’s entire value if it
is implemented, while it fully expropriates the minority in any case. The majority will
then only implement projects raising total welfare. That the selection of projects becomes
efficient when transaction costs disappear indicates that the Coase Theorem has bite, even
if only a fraction m of the members has political power.
Proposition 1: The selection of projects is always optimal when transaction costs vanish:
the majority rule does not matter.
The irrelevance of the majority rule might not surprise practitioners in the European
Union. Many decisions are made, even if unanimity is required for several issues. For
example, the Single European Act was implemented despite the fact that the UK, which
opposed the reform, could have vetoed it. Instead, the UK was compensated to accept.
Similarly, issues are not certain to pass just because the majority rule is small. In the
Uruguay round, a liberalization of the Common Agricultural Policy was rejected, despite
the fact that France, as the single opponent, could not formally block the reform.25 That
the selection of projects is independent of the majority rule does not imply, of course,
that countries are indifferent to which rules are used. The UK appreciates its veto, since
it would not have been compensated without it. However, the irrelevance result above
does suggest that the prime importance of the majority rule may not be to select the
right projects. Instead, I argue, the effects on incentives might be much more important.
To emphasize this, and to avoid somewhat ad hoc transaction costs, transaction costs are
henceforth assumed to be negligible.
3.2. Equilibrium Investments
Having solved the legislative game, we are now ready to study the investment decision
on day 1. When member i decides how much to invest xi in order to increase her value
vi of the project, she realizes that a larger vi affects her utility ui in three ways. First,
there is the direct effect, holding ti constant. If the project is implemented, it is certainly
better to be prepared. But ti is not constant: it depends on vi . Notwithstanding if i ∈ M
or i ∈ N, a high vi reduces i’s bargaining power, and ti increases correspondingly. This
is a multilateral hold-up problem which discourages investments. Notwithstanding vi , i’s
utility becomes
¾
½
if i ∈ N
uN ≡ −r
(3.5)
ui =
if i ∈ M
uM ≡ θ+x+r(1−m)
m
if the project is good. Otherwise, the selection of M is random and each member’s
expected utility is zero.
25
For discussions of these cases, see George and Bache (2001).
11
As a third effect, whether i ∈ M or i ∈ N is also depending on vi . A high vi might
increase i’s political power since, as argued above, a high vi makes i a more attractive
coalition partner, and less likely to be neglected as a minority member. Anticipating that
the other members’ values are uniformly distributed with mean θ + x and density 1/h, i
realizes that her probability of becoming a majority member is
p(xi ) = Pr (vi ≥ vm ) = m +
1
(xi − x) ,
h
(3.6)
if m < 1 and θ ≥ −x.
Member i’s problem is
a+ σ2
Max
xi
Z
[p(xi )uM + (1 − p(xi )) uN ]
dθ
− c(xi ),
σ
(3.7)
−x
which gives the first-order condition
q
q
c (b
xi ) = (uM − uN ) =
h
h
0
where
a+ σ2
q≡
Z
µ
ve + r
m
¶
,
1
1
dθ
= (a + x) +
σ
σ
2
(3.8)
(3.9)
−x
is the probability of a good project and
1³
σ´
ve ≡ E [θ|θ ≥ −x] + x =
a+x+
2
2
(3.10)
is the expected value of a good project.26 The second-order condition is trivially fulfilled.
Since the left-hand side of (3.8) increases in x
bi , i’s optimal investment x
bi decreases
with the majority rule m. With a smaller majority rule, there is less need to compensate
26
An interior solution is implicitly assumed for xi . To be exact, however, (3.6) should be written as


if m + (xi − x) /h < 0

 0
m + (xi − x) /h if m + (xi − x) /h ∈ [0, 1]
,
p(xi ) =


1
if m + (xi − x) /h > 1
which makes the solution to (3.7) xi = x − h(1 − m) ⇒ p(xi ) = 1 if m + (b
xi − x) /h > 1, where x
bi is
defined by (3.8). This can clearly not be the the case for all members (since then xi = x): x would
increase until m + (b
xi − x) /h < 1 and the solution becomes interior. Since p(xi ) is not concave in the
entire interval, the local optimum x
bi should be compared to the other local optimum of xi = 0, if this
makes m + (xi − x) /h < 0. xi = 0 is the better choice if qp(b
xi )(uM − uN ) < c(b
xi ). If an increasing
number of members choose xi = 0, x decreases, which in turn decreases q and uM but increases p(b
xi ). If
the overall effect on qp(b
xi )(uM −uN ) is negative, we might have multiple equilibria where all agents either
invest or not. The chance to have a good equilibrium (where members invest) decreases in m. If the
overall effect is positive, we might have a mixed equilibrium where only some members invest. Though I
rule out such cases here, see Section 4.5 where I allow members to be heterogeneous at the investment
stage. Then, both corner solutions of xi exist in equilibrium.
12
losers within the majority coalition and the number of minority members (which the
majority can expropriate) is larger. Moreover, since the size of the majority coalition
m decreases, the surplus per member of the coalition increases. For these reasons, if m
decreases, the gains from political power increase, as do the incentives to invest. For
a small m, the members may invest considerably in their race for political power. For
a large m, the benefit of political power is low and the hold-up problem ensures that
investments are low. The investment x
bi increases in the enforcement capacity r, because
a larger r reduces the payoff of the minority, while it increases the surplus shared within
the majority. This increases the value of political power. A smaller heterogeneity h
further encourages investments, since even a marginally larger vi then raises the chances
of becoming a majority member quite considerably.
The first-order condition (3.8) shows that i’s investment increases in the probability
q of a good project. Unless the project is good, the majority coalition will be random
and the investment is useless in generating political power. For a fixed probability q,
the incentives to invest also increase in the expected value ve of a good project, since
a larger ve increases the value shared within the majority. This makes i more eager to
become a majority member, and to increase this probability, i invests more. Combined,
(3.8)-(3.10) show that i’s optimal investment x
bi increases in the project’s average value
a for two reasons: first because a larger a increases the probability q of the project being
implemented, and second because a larger a increases the benefits ve shared within the
majority. i’s investment increases in the average level of investment x for the same two
reasons, since x and a have identical effects on the project’s value ex post. This raises the
question of whether the equilibrium is stable. Consider the equilibrium defined by (3.8)
and x
bi = x = x
b, namely
´
1 ³
σ´³
σ
c0 (b
x) =
a+x
b+
a+x
b + + 2r .
(3.11)
2mhσ
2
2
The equilibrium is stable indeed if c is sufficiently convex, which I henceforth assume.27
We can then state:
Proposition 2: Equilibrium investment x
b increases in the project’s value a and the club’s
enforcement capacity r but decreases with ex post heterogeneity h and the majority rule
m, if m < 1. If m = 1, x
b = 0.28
27
The equilibrium is stable if ∂xi /∂x ≤ 1 in (3.8), which requires that c00 (b
x) ≥ (a + x
b + r + σ/2)/hσm.
If c (0) = 0 and a + σ/2 > 0, then the right-hand side of (3.8) lies above the left-hand side for xi =
x = 0. The first time the left-hand side crosses the right-hand side when x increases, c0 crosses from
below, which ensures that this fixed point is a stable equilibrium. That ∂xi /∂x ≤ 1 also guarantees
that the parameters’ effects on x
bi , for x fixed, are similar for the equilibrium x
b. The explanation for
this derives from implicitly deriving xi w.r.t. an arbitrary parameter z where c0 (xi ) = f (x, z). This
gives c00 (xi ) (dxi /dz) = fx (dx/dz) + fz and since dxi /dz = dx/dz in equilibrium, this implies that
dx/dz = fz /(c00 (xi ) − fx ). Strict stability requires that ∂xi /∂x < 1 ⇒ c00 (xi ) > fx , which ensures that
sign (dx/dz) = sign (fz ).
28
Note the discontinuity in x
b when m increases to 1. While x
b might be substantial even if m is just
marginally smaller than 1, x
b drops to zero if m becomes exactly 1. The reason is that if m = 1, i is
certain of becoming a majority member even if vi is the lowest value by far. Political power is guaranteed
and the hold-up problem ensures that i has no incentives to invest. If instead m < 1, i knows that some
0
13
If the majority rule is large, investments are low and few projects turn out to be
worthwhile implementing. Hence, a large m creates a status quo bias because members
do not invest sufficiently. This contrasts the conventional wisdom (see e.g. Buchanan and
Tullock, 1962), arguing that the status quo bias under a large majority rule is due to a
less frequent selection of projects ex post. Then, the Convention’s proposal of a reduced
m should not have any effect before this rule is implemented in 2009. According to the
model above, instead, the proposal should have immediate effects on incentives.
Proposition 2 suggests that the incentives to prepare for a project depend on the
particular project’s value. Information technology, for example, is one of the largest and
fastest growing sectors of the EU, accounting for over 5% of Europe’s GDP. In line with
Proposition 2, CEPR (1999) reports that telecoms is also the most advanced network
industry in terms of domestic deregulation.
3.3. The Optimal Majority Rule
At the constitutional stage, the members select the majority rule maximizing their expected utility, recognizing that the majority rule will affect the incentives to invest. Since
all the members are identical at this stage, they simply prefer the optimal majority rule.
To find this optimal majority rule, the equilibrium investment level x
b in (3.11) should be
∗
compared to the socially optimal investment level x defined by (3.2). While this optimal
investment level is obviously independent of the majority rule m, equilibrium investment
is not. For a larger m, more project-losers must be included in the majority coalition,
and these need to be compensated. Moreover, the minority exploited by the majority is
smaller, and the majority’s surplus is shared between more members. For these reasons,
political power motivates little and the hold-up problem dominates. Members are then
likely to underinvest. If the majority rule m is very small, the majority coalition consists
of an elite where each member receives a large share of the total surplus. Few losers need
compensation and a large minority can be expropriated. This makes political power very
attractive, and its prospects encourage investments more than it is discouraged by the
loss of bargaining power. Members are then likely to overinvest. These opposing forces
are appropriately balanced if the majority rule makes x
b = x∗ . Comparing (3.2) and (3.11)
reveals that this requires
m∗ = (e
v + r) /h = (a + x∗ + 2r + σ/2) /2h,
(3.12)
if the resulting m∗ < 1.29
members will be excluded from the majority, and this will be the members with the smallest vi . Even if
i’s probability of being excluded from the majority is very small, this probability decreases by 1/h if xi
increases by one marginal unit. However, if the inividual shock i had a bell-formed probability density
function, then, as m → 1, Pr(vi < vm ) is approaching zero, as is the equilibrium investment x
b. There is
then no discontinuity.
29
If the m∗ defined by (3.12) is such that m∗ ≥ 1, implying that there is overinvestment for any m < 1,
the optimal investment level x∗ is not attainable by a pure (non-random) majority rule. The second-best
choice is then either the majority rule m = 1, making x = 0 in equilibrium, or a marginally smaller
majority rule which implements the x
b defined by (3.11) and m = 1. The latter is the better choice if
q(b
x)e
v (b
x) − c(b
x) ≥ q(0)e
v (0). If the individual shock i has a bell-shaped probability density function,
however, x
b approaches zero as m approaches 1. Then m∗ ∈ (0, 1) always applies. For this reason, I
henceforth assume m∗ to be interior.
14
If the heterogeneity h is small, the members’ values are closely concentrated. By
investing just a little, i can then increase her probability of becoming a majority member
by quite a lot. The individual return to investments is then high. If the enforcement
capacity r increases, the minority is expropriated more and it becomes more attractive
to be a majority member sharing these revenues. If there is an increase in the project’s
value a, it is possible to tax the minority more and the larger total surplus shared by
the majority coalition makes political power more beneficial. Any of these changes make
gaining political power more easy or attractive, and the incentives to invest increase. To
prevent overinvestments, the majority rule should increase.30,31
Proposition 3: The optimal majority rule m∗ (3.12) increases in the project’s value a
and the club’s enforcement capacity r, but decreases in ex post heterogeneity h.
This result states that political issues of small average values but large heterogeneities
should be taken by small majority rules. The EU’s Common Agricultural Policy and its
structural funds are characterized by distribution and resemble zero-sum games, while
the heterogeneity in preferences typically is large. Such decisions can currently be taken
by a qualified majority. International agreements, however, are package deals likely to
spread the benefits more evenly, and they are typically (according to economists) of large
average value. In line with the theory, such decisions are indeed taken by a larger majority
rule in the EU (namely by unanimity). Less important issues (which are likely to have
low values) can, as Proposition 3 recommends, be taken by a simple majority (by the
Commission). As the EU expands, heterogeneity is likely to increase and the optimal
majority rule should decrease. This fits the recent history as well as the Convention’s
current proposal.32,33
4. Extensions
Since the model in the previous section is both general and simple, it is a useful starting
point for studying other issues. This section employs the model to analyze strategic
delegation, externalities, alternative legislative games, and heterogeneity in size and initial
conditions. All the various extensions start from the model in Section 2, and they can
30
By (3.12), m∗ increases in x∗ . Since x∗ is increasing in a, the positive effect of a on m∗ is reinforced.
The variance in the aggregate shock, σ, has an ambiguous effect on m∗ . On the one hand, σ increases ve
given x, thus increasing m∗ . On the other hand, q decreases in σ if a + x > 0, which in turn decreases
x∗ and thus m∗ . If σ is large, the first effect dominates, and if a is small, both effects are positive. If
2
c(x) = kx2 /2, ∂m∗ /∂σ > 0 if and only if (kσ − 1) > (ka + 1).
31
The positive effect of a and the negative effect of h on m∗ are in contrast to Proposition 1 in Aghion,
Alesina and Trebbi (2004).
32
If the EU’s enforcement capacity r increases over time, however, the optimal majority rule should
increase, according to Proposition 3. If there were a finite number n of members, then the hold-up problem
would not be complete, since a member would expect to receive 1/n of the return of her investments. As
n grows, the hold-up problem increases, and investments fall. Then, the optimal majority rule decreases.
Also this fits well to recent history.
33
See Hix (2004) for the current rules. The rules proposed by the European Convention can be found
at http://european-convention.eu.int.
15
be read independently from each other. However, the extensions can be combined in a
straightforward way, and I do discuss their intersections when they are superadditive.
4.1. Strategic Delegation
A central feature of politics is that it is not the agents themselves that are negotiating
and voting; it is their representatives. In such contexts, already Schelling (1956) recognized that a member may want to appoint a reluctant delegate in order to increase her
bargaining power. Since this delegate is less in favor of the project, the member is taxed
less and compensated more notwithstanding if she is in the minority or the majority. On
the other hand, Chari, Jones and Marimon (1997, p. 959) claim that members attempt
to increase the probability that their district is included in the winning coalition by choosing a representative who values public spending more. This subsection argues that these
opposing forces are balanced appropriately exclusively at the optimal majority rule.
Suppose that it is possible for i on day 1 to delegate bargaining authority to some
delegate di with a di higher (or lower, if di is negative) value of the project:34
vdi = vi + di ,
(4.1)
but there might be some convex cost cd (di ) associated with strategic delegation (e.g. due
to distortions).35 If delegation is sincere, however, cd (0) = 0 and c0d (0) = 0.
If d denotes the average strategic delegation, the majority coalition shares the total
surplus (including what is expropriated by the minority) which is θ + x + d + (1 − m)r if
the project is implemented, and (1 − m)r otherwise. The coalition will thus propose to
execute the project if and only if
θ + x + d ≥ 0,
(4.2)
which differs from the social optimality condition (3.1) if d 6= 0. If d > 0, the delegates
are too positive to the project and too many projects will be implemented. If instead
d < 0 , the delegates are too negative and too few projects will be implemented. Thus,
the optimality condition for delegation is
c0d (d∗i ) = 0 ⇔ d∗i = 0.
(4.3)
But in equilibrium, all members will delegate similarly by d. Suppose (4.2) turns out to
be fulfilled (θ large). The delegates’ utilities become
¾
½
if di ∈ N
uN ≡ −r
udi =
.
if di ∈ M
uM ≡ θ+x+d+r(1−m)
m
34
It is important that i delegates before her shock i is realized. Then, i’s choice of di does not dictate
i’s (or di ’s) future political power, since this will also depend on the noise i . Thus, i can be interpreted
as some uncertainty about the delegate’s preferences (or attractiveness as coalition partner), which will
be revealed only after delegation is made. If i can easily and quickly hire or fire her delegate, it might be
more reasonable to allow i to instead delegate after i has been realized. This might, however, undermine
the value of delegating in the first place, since i can then easily replace a delegate which is on the way
of accepting or rejecting proposals counter to the preferences of i. Delegation is then not credible (see
Katz, 1991, for more on this). Nevertheless, this timing is discussed in Section 4.5, where I do allow for
heterogeneity already at the investment stage.
35
Alternatively, di might be restricted to an interval, di ∈ [−D, D]. This would provide similar results.
16
Delegate di ’s principal, i herself, receives the utility udi − di . The lower is di , i ∈ N, the
more tempted is i’s delegate to reject the project and the less the majority dares to tax
i. The lower is di , i ∈ M, the less eager is i’s delegate to implement the project and the
more of the total surplus is she able to obtain. Delegating by reducing di is therefore
useful for increasing i’s bargaining power.
If θ < −x − d, the initiator anticipates that the project will not be implemented, and
the majority coalition will be randomly drawn. If θ ≥ −x − d, the initiator prefers to
form a majority coalition with those m delegates most in favor of the project, for the same
reason as before. The probability of i’s delegate becoming a coalition member is then
p(xi , di ) = m +
1
[(xi + di ) − (x + d)] .
h
Delegating by increasing di is therefore useful for increasing i’s political power.
Anticipating the effects on bargaining power and political power, i’s problem becomes
a+ σ2
Max
xi ,di
Z
[p(xi , di )(uM − di ) + (1 − p(xi , di )) (uN − di )]
dθ
− c(xi ) − cd (di )
σ
−x−d
which gives the first-order conditions36
¶
ved + r
q
c (b
xi ) =
hm
¶
µ
³ ´
ved + r
0
b
cd di =
q−q
hm
µ
0
where
a+ σ2
q=
Z
(4.4)
(4.5)
dθ
σ
−x−d
is the probability of the project being accepted and
vd = x + d + E [θ|θ ≥ −x − d] = (a + x + d + σ/2) /2
e
is the delegates’ average value of an accepted project.
Comparing (4.4) and (4.5) to the optimality conditions (3.2) and (4.3) shows that
the optimal majority rule m∗ is defined as before by (3.12), and that this ensures sincere
delegation in addition to optimal investments.
Proposition 4: For m > m∗ , members delegate to someone less in favor of the project
(d < 0) and too few projects will be executed. For m < m∗ , members delegate to someone
more in favor of the project (d > 0) and too many projects will be executed. Members
delegate sincerely (d = 0) only at the optimal majority rule m∗ in (3.12).
36
The second-order conditions are trivially fulfilled. For simplicity, an interior solution is assumed and
the equilibrium (where xi = x and di = d) is assumed to be stable. The determinants of x
bi and dbi then
b See the footnotes in Section 3.2 for further remarks on this.
determine the equilibrium x
b and d.
17
Though the result above is remarkably comforting, its intuition can easily be explained.
Notwithstanding if a member considers to delegate or invest, her action has three possible
effects. First, it may directly affect i’s utility through vi , abstracting from any transfers.
Second, a higher vdi reduces i’s bargaining power, given her political power. Third, a
higher vdi makes i a more attractive coalition partner and i’s chances of gaining political
power increases. While bargaining power and political power determine the distribution
of surplus, only the first direct effect is of social value. To make the sum of the three
effects equal to the first, the positive effect of vdi on expected political power should
nullify the negative effect of vdi on bargaining power. This condition does not depend
on how vdi is influenced. Thus, the majority rule m∗ also ensures optimal incentives to
make strategic investments or adjustments to the status quo. This further implies that
it does not matter how the status quo is defined (whether or not the project should be
undertaken); the appropriate majority rule ensures optimal incentives in any case.37
In the European Union, different majority rules are used by the Council, the Commission, and the Parliament. While the last two apply simple majority rules, the Council
typically requires qualified majorities or unanimity. Proposition 4 predicts that the representatives in the Council should be more protectionistic (status-quo biased) than the
Commission and the Parliament. This seems to be the case indeed.38
Another interpretation of d is interesting to consider. So far, the analysis relies on
complete and symmetric information. It may be argued, however, that i is likely to
have a better estimate of vi than has any of her opponents j 6= i. Note, first, that
the argument above works in any case, as long as vdi is observable. Thus, m∗ is the
only majority rule which gives the members incentives to reveal their types truthfully by
sincere delegation. Second, abstracting from delegation, (di + xi + θ) may be interpreted
as i’s "announcement" of her expected value xi + θ on day 1. The announcements may
influence the members’ bargaining power and political power, which is also affected by
some noise i . Though I do not provide a bargaining model of asymmetric information,
the results above suggest while announcing a lower value increases i’s bargaining power,
it reduces her chance to get political power. The two opposing forces may be balanced
by the optimal majority rule.
4.2. Externalities
So far in the analysis, one member’s investment has effect on her own value only. More
generally, however, one member’s value of the project might depend on another member’s
action. For example, if country i modernizes and succeeds in creating a more competitive
sector, it may affect the neighboring country j’s value vj of liberalization. If j expects to
import services from i, j’s value vj of trade liberalization might increase when i becomes
more efficient. If instead j fears tough competition from i, j’s value vj of liberalization
37
A previous version of this paper allowed members to invest by yi in the status quo. This is valuable if
the project turns out to be bad. If the project turns out to be good, a larger investment in the status quo
gives i more bargaining power but less political power. Member i’s first-order condition q − (e
v + r)q/hm
coincides with the first-best condition q − 1 if and only if m = m∗ . If m > (<)m∗ , members invest too
much (little) in the status quo.
38
Also for environmental policies, Weale (2002, p. 210) observes that the Parliament has the general
reputation of having a policy position that is more pro-environmental than the Council of Ministers.
18
might be reduced. To capture such effects, let individual values be determined by
vi = θ + (1 − e)xi + ex + i ,
where e reflects a positive (negative) externality of private investment if e > (<)0. The
coefficients are normalized such that the social value of investments is the same as previously, and the optimal level of investment is still defined by (3.2).
Private investments are only undertaken to the extent that they affect private values.
It is easily shown that member i’s optimal investment level, corresponding to (3.8), is
modified to
µ
¶
ve + r
0
xi ) = (1 − e)q
c (b
,
(4.6)
hm
where q and ve are as defined in Section 3.2. If e is positive, then i only captures a
fraction (1 − e) of the total direct effect of i’s investment. The danger is underinvestment.
To motivate sufficient investments, the prospects of political power must become more
attractive. This can be done by reducing the majority rule, since this decreases the number
of losers that must be compensated and the surplus for each majority member increases.
If the externality is negative, members are instead likely to overinvest. A larger majority
rule is then required to discourage investments. In either case, the first-best investment
level can be achieved by selecting the majority rule inducing x
bi = x = x∗ in (3.2):
m∗e = (1 − e) (e
v + r) /h = (1 − e) (a + x∗ + 2r + σ/2) /2h.
(4.7)
Proposition 5: The optimal majority rule m∗e decreases in the externality e, and it
induces members to internalize the externality.
This result suggests that political issues, characterized by positive externalities of
countries’ investments, should be decided by a smaller majority rule. It is interesting
to note that the common market in the EU was the first area where qualified majority
voting was applied in the EU. According to the Single European Act, e.g. environmental
issues can be decided by a qualified majority according to Article 100a, or by unanimity
according to Article 130s. The latter applies to environmental issues in general, while the
first applies to issues related to the common market. Then, environmental policy is likely
to have spillover effects through trade in addition to cross-border pollution.
Delegation and Externalities
To repeat, i’s choice of effort has three effects on i: the direct effect on vi , the effect on
i’s bargaining power and the prospects for political power. While only the first effect
is of social value, it does not reflect the full social value of the investment when there
are externalities. Making the sum of the effects on political power and bargaining power
zero is not sufficient to ensure optimality, instead, this sum should be set equal to the
externality that we want to internalize. But when the effects on bargaining power and
political power do not cancel, Proposition 4 implies that members delegate strategically.
By comparing (4.6) and (4.5), we realize that no majority rule can make them both
coincide with the optimality conditions (3.2) and (4.3).
19
Proposition 6: If there are externalities, no majority rule can ensure both optimal
investments and sincere delegation.
To guarantee optimal investments, m should be reduced (increased) to internalize a
positive (negative) externality. This, however, will induce members to delegate strategically to someone more (less) in favor of the project in order to increase their prospects for
political power (bargaining power). To ensure sincere delegation, m should be set equal
to m∗ , independent of any externalities. But then, no externalities will be internalized.
The optimal majority rule will have to be a compromise, depending on what is most
important: investments or sincere delegation.39
4.3. Legislative Extensions
The legislative game, as described in Section 2, is both simple and specific. Informed
readers might have noticed several discrepancies relative to the European Union, for
example. This section generalizes the legislative game in three ways, all of which better
tie the model to European institutions in particular, and most political systems in general.
While the previous results survive, new insights emerge.
The European Union consists of several chambers, not only the Council as assumed
above. Indeed, most proposals are negotiated in the European Commission before they are
submitted to the Council which, in turn, has small possibilities of making amendments.40
Also the European Commission consists of national representatives. The majority rule
m applied by the Commission is typically smaller (m = 1/2) than the majority rule m
applied by the Council. To reflect this legislative design, suppose the initiator in the
Commission first selects a minimum-winning coalition M ⊂ I of mass m (relative to the
Commission’s size) which negotiates a proposal. All members of M must agree before
the proposal is submitted as a take-it-or-leave-it offer to the Council. The proposal is
implemented if a fraction m in the Council approves the proposal, while everyone accepts
(ui ≥ −r∀i). This generalization fits most bicameral political systems, but it can also
be interpreted differently: Even with one chamber, the initiator might want to select a
coalition of size m 6= m, different than the majority rule. Thus, this extension may be
interpreted as a relaxation of Riker’s (1962) minimum-winning-coalition assumption.
Second, the initiator, as a president, might have excessive bargaining power. Instead
of assuming, as above, that all coalition-members have equal bargaining power, it is likely
that the president can suggest the first proposal. Only if this offer is rejected will a
randomly drawn coalition-member make another proposal. If there is a discount factor δ
between successive offers, then the initiator is able to capture a share (1 − δ) of the total
surplus. The other members of M receive equal shares of the remaining fraction δ. More
power to the president is reflected by a smaller δ.41
39
It is interesting to notice that when the vi s are private information, there does not exist any mechanism that can solve this trade-off in a better way. Some majority rule can always replicate the mechanism.
40
The EU is tricameral including the Parliament. At the present rules, however, the Parliament is of
less importance, and investigating it is thus relegated for future research.
41
Kirchner (1992, p. 80) discusses the President’s role in the EU. He finds that there is a great deal of
collaboration between the Presidency and the Commission in the setting of the six-monthly priorities.
20
Third, the Convention suggests rotating representation in the European Commission.
There are supposed to be 15 commissioners with a vote and 15 without. Countries will
take it in turns, in strict rotation, to have one of the proper jobs. Suppose that member
i is represented in the Commission with probability li only. With probability 1 − li , i
has no representative in the Commission, and i ∈
/ M notwithstanding vi . With these
generalizations, the model can be solved by backward induction as above.
While member i ∈ M have political power as previously, member j ∈ I\M just
responds to the take-it-or-leave-it offer made by M. To implement the policy as cheaply
as possibly, M expropriates the minority of mass 1 − m by giving them the reservation
utility of −r. In any case, their approvals are superfluous. All other members receive a
utility of exactly zero - just sufficient to make them approve the project. If the project is
to be implemented, any initiator prefers as coalition partners (to M) those m members
(represented in the Commission) most in favor of the project. To reduce the amount of
compensation, the minority not compensated to approve the project will be the 1 − m
members least in favor of the project. The argument for this coalition formation is similar
to that in section 3.1.42 When transaction costs are negligible, M prefers to implement
the project if and only if it increases total welfare. Proposition 1 survives.
Assume, for a moment, that all members invest the same amount x, such that their
values of the project become uniformly distributed with mean θ + x and density 1/h.
Anticipating this, i expects the probability of i ∈ M to be
·
¸
1
p(xi ) = li m + (xi − x) ,
h
while the probability that i becomes a minority member is 1 − p(xi ) as before (3.6). If
θ ≥ −x, the project is implemented and i’s payoff becomes


with probability 1 − p(xi )

 uN = −r
uM = 0
with probability p(xi ) − p(xi )
,
ui =


uM = δ [θ + x + r(1 − m)] /ml with probability p(xi )
since the mass of M is ml if l is the average li . At the investment stage, i’s problem
becomes
a+σ/2
Z
£
¤ dθ
− c(xi )
Max
p(xi )uM + (1 − p(xi ))uN
xi
σ
−x
with the first-order condition
¸
·
q li δ
c (b
xi ) =
(e
v + r(1 − m)) + r ,
h lm
0
where q and e
v are as defined in Section 3.2. Thus, Proposition 2 continues to hold, but
there are three new effects. First, i’s investment decreases in both m and m, since both
kinds of majorities require that losers are compensated instead of being expropriated by
the majority. Second, i invests less if the president is powerful (δ small), since this reduces
42
Formally, the argument justifying this coalition formation requires some marginal transaction costs.
21
the benefit of becoming a majority member. Third, i invests less if li is low relative to l.
If li is small, her representation in the Commission is quite unlikely, and vi is less likely to
influence i’s political power. This can be compensated by a smaller l, however, since then,
the total surplus is shared among a small mass of Commission members ml. Investments
are optimal if x
bi = x∗ (defined as previously by (3.2)) requiring that
mr m l ³
r ´ ve + r
+
=
.
1−
h
δ li
h
h
(4.8)
The solution for m is interior only if the parenthesis is positive, which I thus assume.
While Proposition 3 continues to hold, (4.8) shows that the two majority rules m and m
are substitutes. Incentives remain optimal even if m increases, provided that m decreases
accordingly. To encourage sufficient investments, m should decrease if the president becomes more powerful (δ decreases). This is, indeed, the combination proposed by the
Convention.43
Proposition 7: Member i’s investment decreases in the majority rules m and m, the
president’s power (1−δ), the size of the commission l, but increases in her own probability
of being represented li . Thus, the optimal majority rule m (m) decreases in δ and m (m),
and rotating representation is of no importance if li = l∀i.
4.4. Heterogeneity in Size
Heterogeneity in size is easily motivated. In the European Union, constitutional debates
quite often separate large (e.g. Germany and France) from small (e.g. Belgium and
Denmark) nations. In corporate governance, some shareholders own more shares than
others.While the size of a small member is normalized to one, suppose a fraction k of
all members to be of size z > 1. To simplify, assume that the following per capita
measures are independent on size: the value of the project, reservation utility, and cost
of investment. Thus, if the project is implemented, the total utility of a large member
is uzi = zvi − ti , such that per capita utility is vi − ti /z. If a member is in minority, the
per capita utility is −r, and a large minority member is taxed by ti = z (vi + r). That
the reservation utility is the same per capita indicates that the per capita benefit from
continuing cooperation is the same for all, or that a member failing to implement an
approved project faces a fine proportional to its size.
Whatever is the majority coalition, the majority expropriates the minority and shares
the surplus equally, just as before. But whom will the initiator select as majority members? In the majority coalition, a large member negotiates with one voice, just as the
others, and ends up with the same utility uM .44 This implies that ti = zvi −uM . Thus, the
cost of inviting a large member to the coalition, instead of expropriating it as a minority
43
An earlier version of this paper discussed the stability of coalitions. If coalitions were quite stable, in
the sense that they are formed independently of the particular project, then investments are less likely to
affect political power. Members invest less, and the majority rule should be smaller. This characterizes
most national parliaments.
44
Thus, a large country has a lower per capita bargaining power. This reflects the well-known feature,
observed by e.g. Wallace (1989, p. 202), that small parties often do disproportionately well out of coalition
bargaining.
22
member, is uM + zr. The cost of inviting a small member, by contrast, is only uM + r.
Hence, with equal voting weights, small members will be preferred as coalition partners.
If m < 1 − k, the initiator does not need to include any large members in her coalition,
and large members lack incentives to invest as they cannot gain political power in any
case.
Suppose, instead, that larger members have proportionally more voting power (using
the one-share-one-vote principle). The alternative to inviting one large member is then
to invite z small members, which costs z (uM + r). Then, large members are preferred as
coalition partners. If m < k, small members do not invest as they cannot gain political
power in any case.
To give all members incentives to invest, the initiator must be indifferent between
inviting a small and a large member that both have a high value of the project. Suppose
the voting power of a large member to be w. For two members with the same value
of the project, the initiator is indifferent to their size if uM + zr = w (uM + r), i.e., w
should be a weighted average of the principle one-member-one-vote, and the alternative
proportionality (or one-share-one-vote) principle:
µ
¶ µ
¶
r
uM
w=z
+
.
(4.9)
uM + r
uM + r
Only under such weights do all members have incentives to invest. If the enforcement
capacity r increases, or uM decreases (since e.g. the remaining projects become less
valuable), the weights should be more proportional to size.
Another solution is to use both principles, and require that a political proposal must
fulfill two criteria: First, it must be approved by a fraction m (= 1/2) of all members. If π 1
and π z denote the mass of small and large members that approve the project, respectively,
this condition can be written as:
π1 + πz ≥ m
(4.10)
Second, the set of members that approve the project must contain a required mass (or
population):
π1 + zπ z ≥ mP .
(4.11)
As noted above, to fulfill (4.10), the initiator prefers to select small members as coalition
members. To fulfill (4.11), instead, large members are preferred. To give both large and
small members incentives to invest, both (4.10) and (4.11) must bind in equilibrium.45
This requires:46
m < mP < mz.
(4.12)
45
46
If both (4.10) and (4.11) hold with equality,
π1
=
πz
=
mz − mP
z−1
mP − m
.
z−1
To see this, just apply the previous footnote and require π 1 , π z > 0.
23
Moreover, for small and large members to face the same chance of becoming majority
members, it is required that mP = m(1 − k + kz), where (1 − k + kz) is the total
population.47
To summarize, to give both small and large members some incentives to invest, it
is sufficient with regressive voting weights (4.9) or double majority rules for both the
number of members and the mass they contain (4.12). But does this ensure that the
incentives are the same for small and large members? As before, small members invest
until c0 (xi ) = q (uM + r) /h. Large members invest less, however, since they do not have
proportionally larger bargaining power over the total surplus.48 The problem of large
members is:
a+ σ2
Z
dθ
− zc(xi ) ⇒
[p(xi )uM − (1 − p(xi )) rz]
Max
xi
σ
−x
´
q ³ uM
+r .
xi ) =
c0 (b
h z
How can we ensure that both large and small members invest optimally? Suppose we
introduce the extensions of the legislative game proposed in the previous section. Let small
and large members be politically represented with probabilities l1 and lz , respectively. The
investments of small and large members become
·
¸
q l1 δ
0
c (b
xi ) =
(e
v + r(1 − m)) + r
h l m
¸
·
q lz δ
0
xi ) =
(e
v + r(1 − m)) + r .
cz (b
h zl m
Thus, to ensure the optimal investment level by both large and small members, representation should be proportional to size:49
(4.13)
lz /l1 = z.
By substituting this equality in the above equations, and by setting these equal to the
optimal investment level, the results of Propositions 3 and 7 are confirmed. To summarize
the results of this section, instead:
47
This can be seen by solving
π1
1−k
mz − mP
(z − 1) (1 − k)
48
=
=
πz
⇒
k
mP − m
.
(z − 1) k
If the number of members, n, were finite, then, as noticed in footnote 32, the hold-up problem would
not be complete. Moreover, the hold-up problem would affect large members less, since they would be
able to influence the total value more, of which they can expect to receive 1/n. Thus, large members
may invest more than small members. But as n grows, this effect vanishes.
49
Of course, members disagree over such weights in isolation, as recently demonstrated by the failure
to agree on a constitution for Europe. With side payments available at the constitutional stage, however,
the optimal constitution is likely to be the outcome. Thus, Financial Times states on December 15th (p.
4) that Mr Schröder will now hope German threats of financial retribution will force Spain and Poland
to back down when treaty talks finally resume.
24
Proposition 8: To ensure that both small and large members have incentives to invest,
the voting weights (4.9) should be regressive in size, or majority rules for the number
of members and their mass should be combined (4.12). In addition, to ensure first-best
incentives, the probability of being represented politically (4.13) should increase in size.
The European Union is indeed using regressive voting weights currently,50,51 while
the US is using a double majority system where both the House and the Senate must
approve policies. The European Convention suggested to employ the double majority
rule system as well, setting m = 0.5 and mP /(1 − k + kz) = 0.6, thus favoring large
countries. Interestingly, the Irish presidency of the EU recently recommended that m =
mP /(1 − k + kz) = 0.55. Still, the problem with a double majority rule system is that
countries of intermediate size will be least preferred as coalition partners. They will not
have incentives to invest and they are worse off. This explains why the medium-sized
countries in the EU (Spain and Poland) currently oppose the jproposed double majority
system.
4.5. Heterogeneity in Preferences
In the simple model, all members were assumed to be identical at the investment stage.
This does not characterize Europe very well. Even though countries can alter their competitiveness by domestic investments, some countries are simply more likely to gain from
a project than others. This may reflect previous policies, such as the UK’s privatization
effort under Margaret Thatcher. Alternatively, it reflects differences in natural conditions,
as might be the case for Scandinavia’s stance in agricultural politics. Thus, already at the
investment stage, some countries may be certain of gaining, while others may certainly
lose if some project is executed. If these countries cannot influence their political power
at the legislative stage, the hold-up problem induces them to prepare too little.
Let individual values now be given by vi = θ + ai + xi + i , where the ai s are known
by everybody at the time when the xi s are chosen, and the average ai is zero. This
modification of the model may be interpreted as an alteration of the timing, where some
of the individual shock is revealed before investments are chosen.52
As before, the majority coalition offers the minority their reservation utility only,
shares the total surplus equally and implements only good projects. This coalition consists
of the m members most in favor of the project: M = {i ∈ I|vi ≥ vm } for some vm .53 If
50
In fact, the existing system is much more complex than weighted votes. For a decision to be taken,
there are requirements on the approval number of (weighted) votes, the number of countries, and the
associated size of the population. For most cases, however, only the first of these will bind (Baldwin and
Widgren, 2003).
51
Barbera and Jackson (2004b) provide another explanation for regressive voting schemes. In their
model, a large country is more heterogeneous, and its value vi is therefore more concentrated around its
expected value. This is of no importance for the optimal weights if there are side payments, however.
52
If there were externalities, and vi = θ + (1 − e)xi + ei x + i , then heterogeneity w.r.t. the ei s has the
similar effects as heterogeneity w.r.t the ai s, discussed here.
53
vm is implicitly defined by the requirement that the mass of agents i s.t. vi ≥ vm must equal m, i.e.:
R h/2
R
m = i∈[0,1] vm −ai −exi (d i /h) dF (ai ) where the ai s are distributed with cdf F (ai ).
25
the project turns out to be good, i’s probability of obtaining political power is


if (ai + xi + h/2 − vm ) /h < 0
 0

(ai + xi + h/2 − vm ) /h if (ai + xi + h/2 − vm ) /h ∈ [0, 1]
.
p (xi , ai ) =


1
if (ai + xi + h/2 − vm ) /h > 1
As previously, i’s problem on day 1 is given by
a+ σ2
Max
xi
Z
[p(xi , ai )uM + (1 − p(xi , ai )) uN ]
dθ
− c(xi ),
σ
−x
where uM and uN are still given by (3.5). It is straightforward to show that the solution
to this problem is
xi = 0
c0 (xi ) = c0 (b
x) ≡ q (e
v + r) /mh
xi = h/2 + vm − ai
xi = 0
if
if
if
if
ai
ai
ai
ai
< aA
∈ [aA , aB ]
∈ (aB , aC ]
> aC
where the critical values aA < aB < aC are defined by
hc(b
x)
h
−x
b − + vm
q (uM − uN )
2
h
≡
b
+ vm − x
2
h
+ vm .
≡
2
aA ≡
aB
aC
Member i’s investment is x
b only if i’s initial value ai is in the intermediate interval [aA , aB ].
If i’s ai is lower than aA , i does not find it worthwhile to invest to have a chance of
becoming a majority member at the legislative stage. In any case, this probability will be
very small. Having surrendered all chances of political power, i has no incentives to invest
since the majority will, in any case, expropriate her entire surplus. If ai > aB , i is certain
of becoming a majority member even if i does not invest as much as x
b. An investment
of h/2 + vm − ai is exactly sufficient to ensure that i will become a majority member,
even if i should unfortunately be hit by a negative shock i . i therefore invests exactly
the amount guaranteeing political power: a larger value will just reduce i’s bargaining
power and force i to compensate other members of the coalition. The larger is ai , the less
i needs to invest to guarantee political power. If ai = aC , i does not need to invest at all:
i is in any case a certain majority member. For ai ≥ aC , therefore, i does not invest.54
Similar results hold for strategic delegation. If ai is large (small), i is certain (not)
to gain political power, and i appoints a delegate less in favor of the project (choosing
the di < 0 satisfying c0d (di ) = −q) in order to gain bargaining power. i appoints a more
moderate delegate (by increasing di ) only if this may increase i’s political power, which
54
If the distribution of individual shocks were bell-shaped, the level of investments x
bi , as a function of
ai , would also be bell-shaped.
26
Figure 4.1: Only members with intermediate initial values are motivated to invest by the
prospects for political power.
is possible only if ai is in the intermediate range. The equilibrium levels of di resemble
Figure 4.1.
Can this situation be improved? I will now show that these problems can, in principle,
be solved using the same instruments as if the members were of different size. The problem
above is that members with large (small) ai s are too (un)attractive as coalition partners.
But as we learned in the previous section: attractiveness can be modified by voting power.
Suppose member i, with the initial value ai , has voting power wi in the future vote
upon this project. To give all members that have invested the same xi a fair chance of
becoming coalition members, they must all be equally attractive as coalition partners. To
the initiator, this requires that the cost of inviting another coalition member, relative to
the weight of her vote, should be independent of ai . Introducing the same transaction
costs as in Section 3.1, the per capita surplus in the majority is, from (3.3):
R
R
v
dj
+
(v + r)(1 − λ)dj
j
M
NR j
,
dj
M
and, it can be shown, the initiator selects the members with the highest xi +
of those with the highest vi ) as coalition partners if
wi = (γ − λai ) κ,
where κ can be any positive constant and where
R
ve(1 − λ) − N aj λ + r(1 − λ)dj
R
.
γ≡
dj
M
i
(instead
(4.14)
Thus, to give all members a fair chance to earn political power (and be motivated thereof),
members that are (un)likely to be in favor of the project should have accordingly low
27
(large) voting power. If the transaction cost λ is small, the required difference in voting
weights (4.14) is also small.55
There are, as in the previous section, alternatives to adjusting the weights of votes.
Suppose there are a large number of members with initial condition ai . If the political
proposal required, by the constitution, approval from some members with all kinds of
initial conditions ai , the initiator would prefer to collude with those that have performed
best relative to their initial condition. Then, all members are motivated to invest. A
similar solution is to introduce two chambers, as in Section 4.3. Even if a member with
large initial value ai is certain of being included in the broader majority m in the Council,
i might still invest to be included in the more exclusive majority M (of size m < m) in
the Commission. Even if a member with small ai is certain of being excluded from the
majority M in the Commission, i might still invest to be included in the majority of size
m > m in the Council.56
Proposition 9: With heterogeneity in initial values ai , extreme members (ai < aA or
ai > aC ) do not invest. To motivate all members to invest optimally, it is necessary
to allocate more voting power (4.14) to members with low initial value of the project,
or to require that the majority coalition is supported by members with different initial
conditions.
5. Majority Rules and Side Payments
Crucial in the analysis above is the assumption that members may use side transfers to
compensate and expropriate. As argued in the Introduction, such side payments can be
facilitated by issue linkages or redefining the project, and they are likely to appear in
contexts such as the EU. In other contexts, however, members might not be able to use
side payments. So what about majority rules and incentives? This section solves the
game above, all extensions included, for the case without side payments. The outcome is
contrasted to the results above. This comparison is useful both to understand the limits
of the results and shed light on controversies in the literature.
The model is almost the same as in Sections 2-4: only the legislative game is different.
Now, each policy proposal can only specify whether the project is to be implemented; all
transfers are bound to be zero. If the initiator happens to lose from the project, she prefers
a coalition of other losers to ensure the project is not proposed and the vote will never
take place. Assume, however, that at least one alternative can be suggested by the other
members (citizen initiative). Then, some winner of the project proposes to implement it,
and the final vote will be decisive.
55
Though members disagree over such weights in isolation, they should all agree on the optimal solution
at the constitutional stage if side payments are available.
56
Another solution, discussed in the final section, is to make all members uncertain about their future
political power, by delaying the vote further into the future. The range of ai s where xi = x
b is aB − aA =
h [1 − c(b
x)/q (uM − uN )], which is increasing in the variance of i , h. For a sufficiently large h, all
members are uncertain whether they will get political power, all have initial values ai ∈ [aA , aB ] and all
will invest x
b. With Brownian motions (of the i s), the heterogeneity h at the legislative stage increases
in the time to that stage (the i s would of course not be uniformly distributed).
28
As before, projects should be undertaken if and only if θ ≥ −x, and optimal investments and delegation are given by (3.2) and (4.3). Whether the project actually will be
approved depends on whether the number of winners is larger than the required majority.
Suppose the values (vdi − θ) happen to be distributed according to the cdf G (vdi − θ),
and that the shock i is uncorrelated to i’s size.57 Assume vi > −r∀i. The project is
executed if
1 − G(−θ) ≥ m ⇒
θ ≥ b
θ ≡ −G−1 (1 − m).
(5.1)
Thus, the selection of projects depends on the majority rule. The larger is m, the larger is
b
θ, and the fewer projects are executed. If members were identical (ai = 0∀i), they would
invest the same amount and the values vdi would be uniformly distributed with mean
θ + x − d and density 1/h. The project would be implemented if the mass of winners is
larger than m. (5.1) becomes
θ≥b
θ ≡ −x − d + h (m − 1/2) .
(5.2)
Anticipating that d = 0, and comparing with the above optimality condition (3.1), we
notice that the selection of projects is optimal if and only if m = 1/2. That the optimal
majority rule is exactly 1/2 follows from the symmetric distribution of preferences, and
it resembles May’s (1952) Theorem.
If the project is executed, an individual’s utility becomes
ui = (1 − e)xi + ex + θ + ai + i .
Thus, at the stage of investment, a large country’s problem is
a+ σ2
Max
xi ,di
Z
zui
dθ
− zc(xi ) − zcd (di ),
σ
e
θ
while a small country’s problem is obtained by setting z = 1. Independent of size, the
first-order conditions become58
c0 (xni ) = (1 − e) q
c0d (dni ) = 0
where
a+ σ2
q=
57
Z
e
θ
(5.3)
(5.4)
dθ
σ
Voting weights w.r.t. size is then unimportant, since both small and large countries will have the
same distribution of values (if they make the same investments). If i is correlated with size, or the
number of members n is finite, weights should be proportional to size.
58
The second-order conditions are trivially fulfilled.
29
is the probability of the project being implemented.
If there are no externalities, i.e. e = 0, then (5.3) and (5.4) coincide with the first-best
conditions (3.2) and (4.3) given q. Incentives are optimal and delegation sincere, whatever
is the majority rule, the legislative game (m,δ,li ), the size and the initial condition ai .
These results should not come as a surprise: without transfers, only the first, direct, effect
of the investments affects i’s utility. Bargaining power cannot be exploited and political
power has no return. Investments are then optimal and delegation sincere. Externalities,
however, cannot be internalized in this framework.
Proposition 10: Suppose there are no side payments. The selection of projects depends
on the majority rule, but delegation is sincere and incentives are optimal unless there
are externalities. Heterogeneity in size or preferences, or certain aspects of the political
system (m,δ,li ), have no impact.
The result explains the strong emphasis on the selection of projects by the earlier
literature: e.g. Wicksell (1896), Buchanan and Tullock (1962) and Aghion and Bolton
(2003). As shown by the latter contribution (as well as Section 3.1 in this paper), the
selection depends on the majority rule also if side payments exist, as long as there are
transaction costs. Then, the optimal majority rule is likely to depend on the form and
size of these transaction costs, and Mueller (1989, p. 105) suggests that this explains
controversies in the literature. The contrast to the present paper, however, is not only
due to the vanishing transaction costs; most of all, it arises because project-values are
endogenous. By comparing Propositions 1-9 to Proposition 10, the effect of side payments
is isolated. The good news is that the selection of projects is always efficient - whatever
the majority rule (unless there is strategic delegation). The Coase Theorem extends since
the winners can simply compensate the losers. The bad news is that the incentives (and
delegation) may not be optimal - this hinges on the particular majority rule. The side
payments increase investments if the majority is small, while they reduce investments if
the majority is large.59 Instead of ensuring the right selection of projects, the majority
rule should be set such that incentives are optimal. Then, even externalities can be
internalized. However, the majority rule should also reflect other aspects of the political
system, such as the president’s power and bicameralism. Moreover, heterogeneity in size
or initial conditions distort incentives, unless votes are appropriately weighted or double
majorities required.
6. Research Ahead
6.1. A Quick Summary
Motivated by the seminal debate over Europe’s future constitution, this paper takes a
new look on how to take collective decisions in general, and how to choose majority rules
in particular. While the earlier literature emphasizes the importance of selecting the
59
Similarly, the incentive to claim a low value of the project increases when side payments are possible
(under unanimity). As this can lead to costly signaling, I elsewhere (Harstad, 2003) derive conditions
under which side payments are detrimental to total welfare.
30
right projects, I show that the selection is always efficient if side payments are possible.
While the earlier literature takes the individual values of the project as exogenous, I
study the incentives to influence these values. If the majority rule is large, members
underinvest due to a hold-up problem. If the majority rule is small, members overinvest
to gain political power. To balance these incentives, the majority rule should increase
in the club’s enforcement capacity and the project’s expected value, but decrease in the
ex post heterogeneity in preferences. Not only does this optimal majority rule ensure
first-best investments; it also ensure sincere delegation. Positive (negative) externalities
related to the investment can be internalized by a smaller (larger) majority rule, but
members may then delegate strategically. Different majority rules in bicameral systems
are substitutes, and they should decrease in the president’s power. Heterogeneity with
respect to preferences or size should be acknowledged by appropriately weightening the
votes, and smaller members should be represented politically less frequently.
6.2. Empirical Support?
Before relying on its normative recommendations, the model should earn credibility by
comparing some of its predictions with empirical evidence. The main prediction is that a
larger majority rule reduces investments. The European Union, with its various majority
rules across issues as well as time, ought to provide empirical evidence. For example, are
countries preparing more for deeper European integration (requiring a qualified majority)
than for liberalization with third countries (requiring unanimity)? A second set of predictions claim that the investments also depend on the enforcement capacity, the project’s
value, the uncertainty and the heterogeneity. Are these in line with the evidence? With
respect to strategic delegation, I have already argued that the model is consistent with the
fact that the Commission and the Parliament are more pro-integration than the Council.
Still, all these predictions deserve careful investigation.
If we find support for the two sets of predictions above, the normative recommendations for the optimal majority rules follow by deduction. For example, if the telecoms
sector is liberalized fastest because of its highest value, then liberalization of other public
utilities should be taken by a smaller majority rule. Until we know better, it would be
interesting to study if such normative statements also hold as positive predictions. The
concluding discussions in Sections 3.3, 4.2-4.4 suggested this to be the case, but obviously a great deal remains to be done. The negotiations on Europe’s constitution will be
followed with excitement.
6.3. Legislative Games
The legislative game in Section 2 is both simple and special. Although the extensions
discussed in Section 4.3 do generalize the game, much remains to be done. For example,
I abstracted from the possibility that the minority could make amendments or bribe
members of the majority coalition, and the majority coalition was assumed to be stable.
Though I discussed bicameral political systems, the EU is tricameral. At present, the
European Parliament is much less powerful than the Council, but the Convention does
suggest that the Parliament’s role be strengthened. How will this influence the game?
31
A third extension could be to let a subgroup of members go ahead with the project
alone (as is the case for the common currency), without the approval of others. The possibility for such "flexible" integration is currently a hot topic in the EU. At a first glance,
this provides another benefit of becoming a winner of the project, and this possibility
might be a substitute for a reduced majority rule.60
6.4. Timing of the Vote
One political instrument, neglected above, is the timing of the legislative game. Fearing
low investments, why not implement the project already at the constitutional stage? A
project that has already been implemented, or committed to be so, will surely motivate
members to adjust. This strategy is often applied by the EU, e.g. for its liberalization
of gas. The disadvantage of this strategy is that reversing the project might be costly if
it turns out to be bad (θ low). Thus, this strategy creates a trade-off between efficient
incentives (ex ante) and efficient selection of projects (ex post).
Another extension is to let time be continuous, and let members choose their investments at each point in time. Long before the vote, the uncertainty concerning future
values is large, and all members may invest similar amounts. Closer to the vote, some
members become certain about their political power at the legislative stage, while others
become nervously unsure. Then, according to Proposition 9, investments are likely to
diverge considerably.61 If, in addition, the timing of the vote can be renegotiated, a time
inconsistency problem is likely to arise. Close to the vote, investments diverge and are
suboptimal for most members. Then, it is optimal to either vote right away, to give all
incentives to adjust, or delay the vote to the future, to again make everyone uncertain
about their political power at the legislative stage.
6.5. Other Applications
Though the EU has been the leading example in the paper, the model is general and
applies to many contexts. The anticipated project may, for example, be to stabilize
national debt, as in Alesina and Drazen (1991). Ahead of this, each region might be able
to reduce its own regional deficit by choosing the appropriate policy. Such policies will
certainly affect its value of national stabilization at the legislative stage. The lower is the
debt of a region, the more eager it is to stabilize debt also nationally, but the more it will
have to compensate losers ill-prepared for tough financial policies. This generates a holdup problem, and stabilization will be delayed. Applying Proposition 3 above, the solution
is a lower majority rule. Then, stabilization can be implemented without compensating
60
As discussed by Berglöf, Burkart and Friebel (2003), the "threat" to go ahead alone reduces the
hold-up problem when decisions are taken by unanimity. The possibility to form an inner organization
is, to some extent, a substitute for a reduced majority rule and may become irrelevant when the majority
rule is sufficiently reduced. Perhaps afraid of being excluded, CEPR (1999) reports that several candidate
countries (particularly Hungary) is far ahead of many member countries when it comes to liberalizing the
telecoms market.
61
If this is solved by giving ill-prepared members more voting power, as suggested in Section 4.5, a
moral hazard problem arises in advance.
32
all ill-prepared regions. Fearing to be excluded from the majority coalition, regions will
increase their effort to reduce their debt.62
Majority rules are also important in corporate governance. Collective decisions by
shareholders are typically taken by some majority rule. The project under consideration
may be the firm’s investment or production strategy (DeMarzo, 1993), or to act upon a
takeover bid (Grossman and Hart, 1988, Harris and Raviv, 1988). In advance, shareholders may affect their value of the project by e.g. reducing their individual risk (aversion) by
investing in other assets. As suggested by Propositions 2 and 4, the particular majority
rule may influence the shareholders’ investments, their incentives to delegation strategically, and whether they will truthfully reveal their preferences. Moreover, since the
majority rule affects the relative payoff of status-quo biased risk averse shareholders vs.
risk neutral shareholders, the equilibrium ownership will depend on the majority rule.
The larger the majority rule, the more risk averse the owners will be.
62
Interestingly, parliamentary majority rules differ across countries. Mueller (1996) reports that e.g.
Finland’s constitution requires a two-thirds majority for all important decisions, and a five-sixths majority
for decisions involving property rights.
33
References
Aghion, P., A. Alesina and F. Trebbi (2004): "Endogenous Political Institutions", forthcoming Quarterly Journal of Economics 119 (2).
Aghion, P., and P. Bolton (2003): "Incomplete Social Contracts", Journal of the European
Economic Association 1: 38-67.
Aghion, P., M. Dewatripont and P. Rey (1994): "Renegotiation Design with Unverifiable
Information", Econometrica 62 (2): 257-82.
Aghion, P., and J. Tirole (1997): "Formal and Real Authority in Organizations", Journal
of Political Economy 105 (1): 1-29.
Alesina, A., and A. Drazen (1991): "Why are Stabilizations Delayed?", American Economic Review 81: 1170-88.
Anderberg, D., and C. Perroni (2003): "Time-Consistent Policy and Politics: Does Voting
Matter When Individuals Are Identical?", Topics in Economic Analysis & Policy 3 (1):
Article 3.
Axelrod, R. (1970): Conflict of Interest: A Theory of Divergent Goals with Application to
Politics, Chicago: Markham.
Baldwin, R., and M. Widgren (2003): "Decision-Making and the Constitutional Treaty Will the IGC discard Giscard?", CEPS Policy Brief (37).
Barbera, S., and M. Jackson (2004a): "Choosing How to Choose: Self-stable Majority
Rules", forthcoming Quarterly Journal of Economics 119 (3).
Barbera, S., and M. Jackson (2004b): "On the Weights of Nations: Assigning Voting
Power to Heterogeneous Voters", Mimeo.
Baron, D. (1989): "A Noncooperative Theory of Legislative Coalitions", American Journal
of Political Science 33 (4): 1048-84.
Baron, D., and J. Ferejohn (1989): "Bargaining in Legislatures", American Political
Sience Review 83 (4): 1181-206.
Berglöf, E., M. Burkart and G. Friebel (2003): "Reform under Unanimity", Mimeo.
Brueckner, M. (2000): "Unanimity Versus Concensus Bargaining Games: Strategic Delegation and Social Optimality", Mimeo.
Buchanan, J., and G. Tullock (1962): The Calculus of Consent. Logical Foundations of
Constitutional Democracy. Ann Arbor: University of Michigan Press.
CEPR (1999): A European Market for Electricity? Monitoring European Deregulation 2,
London: Centre for Economic Policy Research.
34
Chari, V. V., L. Jones and R. Marimon (1997): "The Economics of Split-Ticket Voting
in Representative Democracies", American Economic Review 87 (5): 957-76.
de Condorcet, M. (1785): Essai sur l"Application de L" Analyse a’ la Probabilite des
Decisions Rendues a’ la Pluraliste des Voix, Paris.
DeMarzo, P. (1993): "Majority Voting and Corporate Control: The Rule of the Dominant
Shareholder", The Review of Economic Studies 60 (3): 713-34.
Enelow, J. (1997): "Cycling and Majority Rule", in D. Mueller, Perspectives on Public
Choice. Cambridge University Press.
Ferejohn, J., M. Fiorina and R. McKelvey (1987): "Sophisticated Voting and Agenda
Independence in the Distributive Politics Setting", American Journal of Political Science
31: 169-93.
George, S., and I. Bache (2001): Politics in the European Union, Oxford University Press.
Green, E. (1994): "Individual-Level Randomness in a Nonatomic Population", Mimeo.
Groseclose, T., and J. Snyder (1996): "Buying Supermajorities", American Political Science Review, 90 (2): 303-315.
Grossman, S., and O. Hart (1986): "The Costs and Benefits of Ownership: A Theory of
Vertical and Lateral Integration", Journal of Political Economy.
Grossman, S., and O. Hart (1988): "One Share-One Vote and the Market for Corporate
Control", Journal of Financial Economics 20: 175-202.
Harris, M., and A. Raviv (1988): "Corporate Governance: Voting Rights and Majority
Rules", Journal of Financial Economics 20: 203-35.
Harstad, B. (2003): "Uniform or Different Policies?", Ch. 3 in Organizing Cooperation:
Bargaining, Voting and Control, Monograph 46, Institute for International Economic
Studies, Stockholm University.
Hart, O., and J. Moore (1990): "Property Rights and the Nature of the Firm", Journal
of Political Economy 98 (6): 1119-58.
Hart, S., and A. Mas-Colell (1996): "Bargaining and Value", Econometrica 64 (2): 357-80.
Hix, S. (2004): The Political System of the European Union, 2nd edn, London: Palgrave
(book will be published in 2004).
Katz, M. L. (1991): "Game-playing Agents: Unobservable Contracts as Precommitments",
Rand Journal of Economics 22 (3): 307-28.
Kirchner, E. J. (1992): Decision-making in the European Community: the Council Presidency and European Integration, Manchester University Press.
35
Krishna, V., and R. Serrano (1996): "Multilateral Bargaining", Review of Economic
Studies 63: 61-80.
Maggi, G., and M. Morelli (2003): "Self Enforcing Voting in International Organizations",
Mimeo.
May, K. (1952): "A Set of Independent, Necessary and Sufficient Conditions for Simple
Majority Decisions", Econometrica 20: 680-84.
McLaren, J. (1997): "Size, Sunk Costs, and Judge Bowker’s Objection to Free Trade."
American Economic Review 87 (3): 400-20.
Mueller, D. C. (1989): Public Choice II, Cambridge University Press.
Mueller, D. C. (1996): Constitutional Democracy, Oxford University Press.
Persico, N. (2004): "Committee Design With Endogenous Information", Review of Economic Studies 71 (1).
Persson, T., and G. Tabellini (1996): "Federal Fiscal Constitutions: Risk Sharing and
Moral Hazard", Econometrica 64 (3): 623-46.
Riker, W. H. (1962): The Theory of Political Coalitions, Yale University Press.
Rousseau, J. J. (1762): On Social Contract or Principles of Political Right. (translated
to English by Bondanella, Conaway, W.W. Norton & Company, 1988).
Schelling, T. (1956): "An Essay on Bargaining", American Economic Review 46 (3):
281-306.
Wallace, H. (1989): "Bargaining in the EC", in Tarditi et. al. (Eds.), Agricultural Trade
Liberalization and the European Community, Oxford University Press.
Wallner, K. (2003): "Specific Investments and the EU enlargement", Journal of Public
Economics 87 (5-6): 867-82.
Weale, A. (2002): "Environmental Rules and Rule-making in the European Union", in
A. Jordan (Ed.), Environmental Policy in the European Union. Actors, Institutions and
Processes, Earthscan Publications Ltd.
Wicksell, K. (1896): "Ein neues Prinzip der gerechten Besteurung." Finanztheoretische
Undersuchungen, Jena: iv-vi, 76-87, 101-59. Translated by J. Buchanan and reprinted
as "A New Principle of Just Taxation" in Classics in the Theory of Public Finance, New
York, St. Martin’s Press (1967): 72-118.
36
Notater | Papers | 2003 – 2004
2003
No. 644
Morten B. Mærli Nuclear Dimensions of the Iraqi Crisis
No. 645
Indra Øverland A Gap in OSCE Conflict Prevention? Local Media and InterEthnic Conflict in the Former Soviet Union
No. 646
Indra Øverland Defusing a Ticking Bomb? Disentangling International
Organisations in Samtskhe-Javakheti
Nr. 647
Per Botolf Maurseth Norsk utenrikshandel, markedspotensial og handelshindre
Nr. 648
Jens Chr. Andvig A Polanyi Perspective on Post-Communist Corruption
No. 649
No. 650
Nr. 651
Nr. 652
Nr. 653
No.654
No. 655
No.656
No.657
Daniel Heradstveit The Rhetoric of Hegemony. How the extended definition of
David C. Pugh terrorism redefines international relations
Jens Chr. Andvig Corruption and fast change: Shifting modes of microcoordination
Leo A. Grünfeld Eksport av tjenester og potensialet for økt verdiskapning i
Norge: En empirisk kartlegging
Hege Medin Regionale og bilaterale handelsavtaler i Latin-Amerika.
Konsekvenser for norsk eksport
Arne Melchior A Global Race for Free Trade Agreements. From the Most to the
Least Favoured Nation Treatment?
Axel Borchgrevink Evaluation of Fadcanic’s teacher training program in
Anníbal R. Rodrígues Nicaragua’s Southern autonomous region of the Atlantic
Coast
Daniel Heradstveit How the Axis of Evil Metaphor Changes Iranian Images of the
G. Matthew Bonham USA
Axel Borchgrevink Study of selected Fredskorpset exchange projects
Leo A. Grünfeld The Intangible Globalization. Explaining the Patterns of
International Trade and FDI in Services
2004
Nr. 658
Arne Melchior EFTAs frihandelsavtaler: Betydning for Norge
No. 659
Pernille Rieker EU Security Policy: Contrasting Rationalism and Social
Constructivism
Nr. 660
Per Botolf Maurseth Tollnedtrapping for industrivarer i WTO – Virkninger for Norge
No. 661
Bård Harstad Uniform or Different Policies
No. 662
Bård Harstad Majority Rules and Incentives. International voting affects
domestic policies
Publikasjoner fra
Norsk Utenrikspolitisk Institutt
Internasjonal politikk
Nr. 2- 2004
Skillet mellom hva som utgjør nasjonal og internasjonal politikk, er i stor grad i ferd med å bli visket ut.
IP ønsker å være helt i front med å utforske denne dynamikken. 4 nummer i året.
Forord: Postsovjetiske ansikter Birgitte Kjos Fonn · Tsjetsjenske separatister – mellom barken og veden
Julie Wilhelmsen · Svalbard: russiske persepsjoner og politikkutforming Jørgen Holten Jørgensen ·
Russisk oljeindustri og Nordflåten – interessekonflikt eller strategisk partnerskap? Kristian Åtland ·
Aktuelt: Georgias roserevolusjon. Forhistorien og etterspillet Indra Øverland · Exodus fra Russland til
Israel Hans-Wilhelm Steinfeld · Utenrikspolitisk utsyn: Norden och EU Paavo Lipponen·Bokspalte ·
Summaries
Abonnementspriser kr 330 [Norge/Norden] kr 450 [utenfor Norden]
Enkelthefter kr 95 pr. hefte + porto/eksp.
Forum for Development Studies
No. 2 - 2003
Forum bringer artikler (på engelsk) om bistandspolitikk, Nord-Sør-forhold og den tredje verden.
To nummer i året.
Introduction · Democratic Decentralisation and Poverty Reduction: Exploring the Linkages Trond Vedeld
· Methodological Individualism and Rational Choice in Neoclassical Economics: A Review of Institutionalist Critique Darley Jose Kjosavik · National Capabilities and Economic Development: A Subjectivist View
Tony Fu-Lai Yu
Debates:
I. DEVELOPMENT RESEARCH CHALLENGES UNDER SHIFTING POLICIES
New Realities, New Strategies Nina Gornitzka · Research Priority No. One: Fighting Poverty Asbjørn
Løvbræk · The Critial Role of Development Research Desmond McNeill
II. INTERDISCIPLINARITY: STILL A CHALLENGE IN DEVELOPMENT RESEARCH
Nina Gornitzka
III. THE MYTHOLOGY OF AID: CATCHWORDS, EMPTY PHRASES AND TAUTOLOGICAL REASONING
Henrik Secher Marcussen and Steen Bergendorff
IV. THE WDR 2004 ON MAKING SERVICES WORK FOR POOR PEOPLE
Application of the WDR 2004 Accountability Model to the HIV/AIDS and Development Agenda
Sigrun Møgedal · Missing Perspectives: People and Gender Torild Skard
V. THE PROS AND CONS OF SELF-RELIANCE: ERITREA’S RELATIONS WITH AID AGENCIES AND NGOS Christine
Smith-Simonsen · Book Review
Abonnementspriser NOK 220 [i Norden] NOK 300 [utenfor Norden]
Enkelthefter NOK 120 + porto/eksp.
Nordisk Øst·forum
Nr. 2- 2004
Nordisk Østforum er et kvartalstidsskrift som vektlegger politisk, økonomisk og kulturell utvikling i ØstEuropa og Sovjet unionens etterfølgerstater.
Forord · Defenestrasjon – ein tsjekkisk politisk tradisjon? Elisabeth Bakke · Den polske venstrefløjssammenslutning SLD – fra partiføderation til et almindeligt politisk parti Søren Riishøj · Blat – mellom
gaver og varer i Moldova Elisabeth L’orange Fürst · Iran i russisk sikkerhedspolitik: kærlighed eller
fornuftsægteskab? Jakob Sørensen & Allan H. Larsen · Demokratiet og dets fiender: holdninger til
demokrati i Baltikum Kjetil Duvold · Kulturmöten och kommunikation i svenskt-baltiskt
utvecklingsarbete Tove Lindén · Velkommen til Internett · Bokomtaler · Nye bøker i Norden
Abonnementspriser kr. 265 [studenter] kr. 330 [privatpersoner] kr. 450 [institusjoner]
Enkelthefter kr 115 pr. hefte + porto/eksp.
Hvor Hender Det?
Hvor Hender Det? (HHD) er et ukentlig nyhetsbrev som gir deg bakgrunn om internasjonale spørsmål i
konsentrert og forenklet form. HHD er det du trenger for øyeblikkelig oppdatering, som en hjelp til å
forklare inntrykk og se dem i sammenheng. I mange fag og sammenhenger har vi behov for kortfattet
framstilling av konflikter og samarbeid, prosesser, utfordringer og utviklingstrekk i det internasjonale
samfunnet. HHD ligger også på Internett. Godt over 100 artikler fra tidligere årganger innenfor en rekke
emner er lagt ut i fulltekst. www.nupi.no/pub/hhd/hhdliste.htm.
Abonnementspriser kr. 260 pr skoleår [2002/2003] kr. 360 pr skoleår [utenfor Norge]
Klasseabonnement kr. 75 pr. ab. [min. 10 eks]
Norsk Utenrikspolitisk Institutt Postboks 8159 Dep. 0033 Oslo
Tel.: [+47] 22 99 40 00 | Fax: [+47] 22 36 18 97 | Internett: www.nupi.no | E-post: [email protected]